Answered
Illustrator Clipping mask [offset path] option?
Hey, I thought I would suck at explaining this very well so I made some reference images to make it less confusing.
See below:

Hey, I thought I would suck at explaining this very well so I made some reference images to make it less confusing.
See below:

One way is to use an "Opacity Mask" instead of a "Clipping Mask". You can use a copy of the top path as a mask on the bottom path. To change the thickness of the mask, just activate the "Transparency Channel" in the Transparency panel and change the thickness of the line.

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